A novel hierarchical nanotube array (NTA) with a massive layered top and discretely separated nanotubes in a core–shell structure, that is, nickel–cobalt metallic core and nickel–cobalt layered double hydroxide shell (NiCo@NiCo LDH), is grown on carbon fiber cloth (CFC) by template‐assisted electrodeposition for high‐performance supercapacitor application. The synthesized NiCo@NiCo LDH NTAs/CFC shows high capacitance of 2200 F g−1 at a current density of 5 A g−1, while 98.8% of its initial capacitance is retained after 5000 cycles. When the current density is increased from 1 to 20 A g−1, the capacitance loss is less than 20%, demonstrating excellent rate capability. A highly flexible all‐solid‐state battery‐type supercapacitor is successfully fabricated with NiCo LDH NTAs/CFC as the positive electrode and electrospun carbon fibers/CFC as the negative electrode, showing a maximum specific capacitance of 319 F g−1, a high energy density of 100 W h kg−1 at 1.5 kW kg−1, and good cycling stability (98.6% after 3000 cycles). These fascinating electrochemical properties are resulted from the novel structure of electrode materials and synergistic contributions from the two electrodes, showing great potential for energy storage applications.